Help pls!!
Set $\overline{N}:=N\cup\{\infty\}$, where $\infty$ is a "point" not in $N$. Define$d$:
$ \overline{N}x\overline{N}\rightarrow \mathbb{R}$ by\\
$d(m,n):= |\frac{1}{n} - \frac{1}{m} |$
$d(n,\infty) = d(\infty, n):= \frac{1}{n} $
$d(\infty,\infty) := 0 $
Show
b) $a$ sequence $a_{n} \in X$ converges to $a \in X$ if and only if the map
$f:\overline{N}\rightarrow X$ defined by\\

$f(n):=a_{n}$
$f(\infty):=a$

is continuous. Hint : Most important is that $f$ is continuous in $\infty$

Question

Help pls!!
Set $\overline{N}:=N\cup\{\infty\}$, where $\infty$ is a "point" not in $N$. Define$d$:
 $ \overline{N}x\overline{N}\rightarrow \mathbb{R}$ by\\
$d(m,n):= |\frac{1}{n} - \frac{1}{m} |$
  $d(n,\infty) = d(\infty, n):=  \frac{1}{n} $
 $d(\infty,\infty)  := 0 $
  Show 
b)  $a$ sequence  $a_{n} \in X$ converges to $a \in X$ if and only if the map 
     $f:\overline{N}\rightarrow X$ defined by\\
       
            $f(n):=a_{n}$
           $f(\infty):=a$
           
           is continuous. Hint : Most important is that $f$ is continuous in $\infty$

anonymous · Answer

What's X?

anonymous · Answer

hmm

anonymous · Answer

You do not know what X is?

anonymous · Answer

defined by
       
            $f(n):=a_{n}$
           $f(\infty):=a$

anonymous · Answer

One has to know where are the a_n's

anonymous · Answer

i think its all given in that question :(